LCM of 2 and 10

LCM of 2 and 10 is the smallest number among all common multiples of 2 and 10. The first few multiples of 2 and 10 are (2, 4, 6, 8, 10, 12, 14, . . . ) and (10, 20, 30, 40, . . . ) respectively. There are 3 commonly used methods to find LCM of 2 and 10 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 2 and 10 is 10.

Explanation:

The LCM of two non-zero integers, x(2) and y(10), is the smallest positive integer m(10) that is divisible by both x(2) and y(10) without any remainder.

The methods to find the LCM of 2 and 10 are explained below.

• By Prime Factorization Method
• By Division Method
• By Listing Multiples

LCM of 2 and 10 by Prime Factorization

Prime factorization of 2 and 10 is (2) = 2¹ and (2 × 5) = 2¹ × 5¹ respectively. LCM of 2 and 10 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 5¹ = 10.
Hence, the LCM of 2 and 10 by prime factorization is 10.

LCM of 2 and 10 by Division Method

To calculate the LCM of 2 and 10 by the division method, we will divide the numbers(2, 10) by their prime factors (preferably common). The product of these divisors gives the LCM of 2 and 10.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 2 and 10. Write this prime number(2) on the left of the given numbers(2 and 10), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (2, 10) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
• Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 2 and 10 is the product of all prime numbers on the left, i.e. LCM(2, 10) by division method = 2 × 5 = 10.

LCM of 2 and 10 by Listing Multiples

To calculate the LCM of 2 and 10 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 2 (2, 4, 6, 8, 10, 12, 14, . . . ) and 10 (10, 20, 30, 40, . . . . )
• Step 2: The common multiples from the multiples of 2 and 10 are 10, 20, . . .
• Step 3: The smallest common multiple of 2 and 10 is 10.

∴ The least common multiple of 2 and 10 = 10.

☛ Also Check:

• LCM of 5 and 13 - 65
• LCM of 34 and 51 - 102
• LCM of 20 and 30 - 60
• LCM of 60 and 80 - 240
• LCM of 4 and 8 - 8
• LCM of 6, 8 and 12 - 24
• LCM of 6 and 18 - 18

FAQs on LCM of 2 and 10

What is the LCM of 2 and 10?

The LCM of 2 and 10 is 10. To find the least common multiple of 2 and 10, we need to find the multiples of 2 and 10 (multiples of 2 = 2, 4, 6, 8 . . . . 10; multiples of 10 = 10, 20, 30, 40) and choose the smallest multiple that is exactly divisible by 2 and 10, i.e., 10.

What is the Relation Between GCF and LCM of 2, 10?

The following equation can be used to express the relation between GCF and LCM of 2 and 10, i.e. GCF × LCM = 2 × 10.

If the LCM of 10 and 2 is 10, Find its GCF.

LCM(10, 2) × GCF(10, 2) = 10 × 2
Since the LCM of 10 and 2 = 10
⇒ 10 × GCF(10, 2) = 20
Therefore, the greatest common factor (GCF) = 20/10 = 2.

Which of the following is the LCM of 2 and 10? 15, 11, 30, 10

The value of LCM of 2, 10 is the smallest common multiple of 2 and 10. The number satisfying the given condition is 10.

What is the Least Perfect Square Divisible by 2 and 10?

The least number divisible by 2 and 10 = LCM(2, 10)
LCM of 2 and 10 = 2 × 5 [Incomplete pair(s): 2, 5]
⇒ Least perfect square divisible by each 2 and 10 = LCM(2, 10) × 2 × 5 = 100 [Square root of 100 = √100 = ±10]
Therefore, 100 is the required number.